2022/09/17 by Yoshino, Kiyoto
#05C50 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2209.08308
In 2020, Lin and Yu claimed to prove the so-called Lemmens-Seidel conjecture for base size 5. However, their proof has a gap, and in fact, some set of equiangular lines found by Greaves et al. in 2021 is a counterexample to one of their claims. In this paper, we give a proof of the conjecture for base size 5. Also, we answer in the negative a question of Greaves et al. in 2021 whether some sets of 57 equiangular lines with common angle \arccos(1/5) in dimension 18 are contained in a unique set of 276 equiangular lines with common angle \arccos(1/5) in dimension 23. In addition, we answer in the negative a question of Cao et al. in 2021 whether a strongly maximal set of equiangular lines with common angle \arccos(1/5) exists except the set of 276 equiangular lines with common angle \arccos(1/5) in dimension 23.